{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,1]],"date-time":"2025-04-01T14:33:01Z","timestamp":1743517981913,"version":"3.40.3"},"reference-count":11,"publisher":"Scientific and Business World","license":[{"start":{"date-parts":[[2012,11,7]],"date-time":"2012-11-07T00:00:00Z","timestamp":1352246400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"National Research Project"},{"name":"Mohamed Boudiaf University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Decision Sciences"],"published-print":{"date-parts":[[2012,11,7]]},"abstract":"<jats:p>We give a hybrid two-stage design which can be useful to estimate the reliability of a parallel-series and\/or by duality a series-parallel system. When the components' reliabilities are unknown, one can estimate them by sample means of Bernoulli observations. Let <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>T<\/mml:mi><\/mml:mrow><\/mml:math> be the total number of observations allowed for the system. When <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>T<\/mml:mi><\/mml:mrow><\/mml:math> is fixed, we show that the variance of the system reliability estimate can be lowered by allocation of the sample size <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>T<\/mml:mi><\/mml:mrow><\/mml:math> at components' level. This leads to a discrete optimization problem which can be solved sequentially, assuming <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>T<\/mml:mi><\/mml:mrow><\/mml:math> is large enough. First-order asymptotic optimality is proved systematically and validated <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>T<\/mml:mi><\/mml:mrow><\/mml:math> Monte Carlo simulation.<\/jats:p>","DOI":"10.1155\/2012\/289035","type":"journal-article","created":{"date-parts":[[2012,11,11]],"date-time":"2012-11-11T06:31:14Z","timestamp":1352615474000},"page":"1-14","source":"Crossref","is-referenced-by-count":2,"title":["An Allocation Scheme for Estimating the Reliability of a Parallel-Series System"],"prefix":"10.47654","volume":"2012","author":[{"given":"Zohra","family":"Benkamra","sequence":"first","affiliation":[{"name":"Department of Physics, University of Science and Technology of Oran-Mohamed Boudiaf (USTOMB), BP 1505 El M'Naouer, Oran 31000, Algeria"}]},{"given":"Mekki","family":"Terbeche","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Oran, BP 1524 El M'Naouer, Oran 31000, Algeria"}]},{"given":"Mounir","family":"Tlemcani","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Science and Technology of Oran-Mohamed Boudiaf (USTOMB), BP 1505 El M'Naouer, Oran 31000, Algeria"}]}],"member":"52777","reference":[{"issue":"4","key":"4","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1109\/24.693781","volume":"46","year":"1997","journal-title":"IEEE Transactions on Reliability"},{"issue":"346","key":"3","first-page":"485","volume":"69","year":"1974","journal-title":"Journal of the American Statistical Association"},{"issue":"2","key":"5","first-page":"1","year":"2002","journal-title":"Southwest Journal of Pure and Applied Mathematics"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-3758(01)00242-7"},{"issue":"412","key":"8","first-page":"1134","year":"1990","journal-title":"Journal of the American Statistical Association"},{"issue":"3","key":"10","first-page":"325","volume":"5","year":"2005","journal-title":"Advances and Applications in Statistics"},{"issue":"3","key":"11","doi-asserted-by":"crossref","first-page":"1358","DOI":"10.1214\/aos\/1176347754","volume":"18","year":"1990","journal-title":"Annals of Statistics"},{"key":"6","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1080\/07474949608836353","volume":"15","year":"1996","journal-title":"Sequential Analysis"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1109\/24.229502"},{"key":"1","first-page":"119","volume":"13","year":"2010","journal-title":"Revue ARIMA"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2010.12.033"}],"container-title":["Advances in Decision Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/2012\/289035.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/2012\/289035.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/2012\/289035.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,28]],"date-time":"2020-09-28T16:09:57Z","timestamp":1601309397000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/archive\/2012\/289035\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11,7]]},"references-count":11,"alternative-id":["289035","289035"],"URL":"https:\/\/doi.org\/10.1155\/2012\/289035","relation":{},"ISSN":["2090-3359","2090-3367"],"issn-type":[{"type":"print","value":"2090-3359"},{"type":"electronic","value":"2090-3367"}],"subject":[],"published":{"date-parts":[[2012,11,7]]}}}